01 - Preheat grill to medium-high heat, approximately 400°F.
02 - Pat chicken breasts dry. In a small bowl, combine olive oil, smoked paprika, garlic powder, onion powder, salt, and black pepper. Coat both sides of the chicken evenly with the seasoning mixture.
03 - Brush husked corn on the cob with melted butter and season with salt and black pepper to taste.
04 - Place chicken breasts on the grill and cook for 6 to 7 minutes per side. During the last 3 to 4 minutes on each side, baste generously with barbecue sauce. Grill until the internal temperature reaches 165°F.
05 - Simultaneously grill corn, turning occasionally, until kernels are tender and lightly charred, about 10 to 12 minutes.
06 - Remove chicken breasts and corn from the grill. Allow chicken to rest for 5 minutes before slicing.
07 - Plate the grilled chicken alongside corn on the cob. Garnish with chopped parsley and lime wedges if desired.